Continuum Mechanics and Thermodynamics最新文献

{"title":"A variational multi-phase model for phase-transforming elasto-plastic materials","authors":"Sarah Dinkelacker-Steinhoff,&nbsp;Klaus Hackl","doi":"10.1007/s00161-026-01487-z","DOIUrl":"10.1007/s00161-026-01487-z","url":null,"abstract":"<div><p>In this work, we suggest a framework for modeling evolution of phase-fractions in elastoplastic materials associated with phase transformations. The model is based on variational principles for inelastic materials. We restrict ourselves to infinitesimal strains and isotropic materials. In our work we employ the so-called dissipation distance, which describes an immediate phase transition in time via an underlying probability matrix. The volume fractions of the various phases are represented by Young measures to obtain a time continuous microstructure evolution. A minimum principle is presented to govern the initiation of new phases. The model is verified employing a two-dimensional benchmark test implemented by the Finite Element Method.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 4","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-026-01487-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148060656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Investigating the functional adaptation response of a fully three-dimensional femur under dynamic loading during distinct physiological activities","authors":"Minku,&nbsp;Koffi Enakoutsa,&nbsp;Ivan Giorgio,&nbsp;Rachele Allena","doi":"10.1007/s00161-026-01489-x","DOIUrl":"10.1007/s00161-026-01489-x","url":null,"abstract":"<div><p>The accurate computational prediction of bone adaptation models primarily depends on loading events that are physiologically relevant. Most previous research has been confined to bone remodelling simulations involving simplified loading instances or focused on specific sections of the femur, particularly the proximal femur. The extent to which different cyclic, time-dependent loadings that occur during daily activities in the human femur affect its functional adaptation has yet to be thoroughly investigated. The objective of this research is to comprehensively analyze the remodelling response of the femur under the combined effects of axial compression, bending, and torsional cyclic loading experienced during different physiological activities, such as walking, stair climbing, jogging, and stumbling. This is achieved by developing a 3D FE model of human femur and employing the diffusion-based continuum bone remodelling approach to predict bone density patterns. The 3D femur is described as a deformable generalized continuum that incorporates porosity and finite deformation with a nonlinear constitutive model. Overall, results revealed significant influence of distinct activity-induced mechanical loads on remodelling dynamics of the 3D femur. The dynamic mechanical loading encountered by the femur in jogging and stumbling activity leads to elevated bone density when compared to stair climbing and walking activity. The distal diaphyseal region experiences the highest gain in bone density, whereas the greater trochanter exhibits poor adaptation response, regardless of loading activity. The findings of the study are beneficial for clinicians in mitigating fracture risk among patients by providing recommendations on clinical intervention strategies based on physical activities.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 4","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148060661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis of a double-layered photo-thermodiffusive semiconducting media with an internal heat source","authors":"Praveen Ailawalia,&nbsp;Marin Marin,&nbsp;Andreas Öchsner","doi":"10.1007/s00161-026-01478-0","DOIUrl":"10.1007/s00161-026-01478-0","url":null,"abstract":"<div><p>The research article investigates the deformation of a double-layered photo-thermodiffusive semiconducting layered structure. The width of both layers is <i>d</i>, and an internal heat source of magnitude <i>Q</i> is acting in the lower layer. The equations of motion are solved by normal mode analysis. The expressions of displacement, stress, temperature distribution, carrier density and moisture concentration are derived by applying appropriate boundary conditions. Numerical investigations are conducted for three different time spans, and the graphical results are generated by developing codes in a mathematical software.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 4","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148060660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling of problems with small-scale liquid inclusions - Influence of initial stress state","authors":"Sofia G. Mogilevskaya,&nbsp;Zhilin Han,&nbsp;Henryk K. Stolarski","doi":"10.1007/s00161-026-01480-6","DOIUrl":"10.1007/s00161-026-01480-6","url":null,"abstract":"<div><p>The problem of a small liquid inclusion within an elastic matrix subjected to initial stress and external load is considered. To evaluate the elastic fields in the material system, the two-stage process is proposed. In each stage, the inclusion/matrix interface is described by the Gurtin-Murdoch model of material surface. Stage I is designed to estimate the initial stresses that develop in all parts of the material system, e.g., during the fabrication process. Stage II represents the analysis of deformations and stresses due to external load. In that stage, the effects of initial stresses are included. The governing equations for the second stage problem are derived by linearization of the non-linear formulation. Three-dimensional equations for the two stages are provided and specified for two-dimensions. To illustrate the approach, the isotropic matrix is considered, the plane strain assumptions are made, and an inclusion is assumed to be of circular shape. Closed-form solutions for the elastic fields in the material system are obtained under two different descriptions of the matrix material. Those expressions are compared with solutions previously reported in the literature.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-026-01480-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148009185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Experimental and numerical study on the effects of temperature variations on sound transmission through cylindrical shells","authors":"Maisam Parhikhteh,&nbsp;Mahdi Karimi,&nbsp;Reza Ahmadi,&nbsp;Omid Mohammadpour","doi":"10.1007/s00161-026-01484-2","DOIUrl":"10.1007/s00161-026-01484-2","url":null,"abstract":"<div><p>Cylindrical shells, widely used in various industries, are frequently subjected to diverse thermal loads that affect their vibrational and acoustic behavior. Consequently, evaluating the acoustic performance of these structures under varying temperatures is crucial. This study investigates the impact of temperature variations on sound transmission through cylindrical shells using a combined approach of experimental testing and numerical analysis. In the experimental phase, a steel cylindrical shell was fabricated and exposed to acoustic waves in an acoustic test chamber, where the transmitted sound pressure levels were measured at different temperatures (e.g., –70 °C, 25 °C, and 80 °C). Concurrently, a finite element model of the cylindrical shell was developed using COMSOL Multiphysics, and vibro-acoustic analyses were conducted across these temperatures. The excellent agreement between experimental and numerical results validated the accuracy of the numerical model and the reliability of the experimental data. Findings indicate that temperature is a critical parameter: as temperature increases, natural frequencies decrease due to reduced stiffness, and the transmitted sound pressure level through the shell significantly rises, particularly observed at higher frequencies and temperatures (e.g., sound pressure levels were notably higher at 80 °C compared to 25 °C and –70 °C). This precise understanding enables the design of optimized structures to mitigate sound and vibration under varying thermal conditions.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148008833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Study of climate change dynamics in vicinity of hemisphere: an analysis of velocity and thermal slip effects","authors":"Farhat Imtiaz,&nbsp;Muhammad Ashraf,&nbsp;Ghulam Rasool,&nbsp;Dalia H. Elkamchouchi,&nbsp;M. Ijaz Khan","doi":"10.1007/s00161-026-01483-3","DOIUrl":"10.1007/s00161-026-01483-3","url":null,"abstract":"<div><p>This study examines the behavior of hybrid nanofluid flow with mixed convection and slip effects near a tilted hemispherical surface with a focus on its influence on climate change. These hybrid nanoparticles are present in large quantities and are unevenly distributed across different regions of the hemisphere. A mathematical model is developed using nonlinear coupled partial differential equations, which are transformed into a dimensionless form through suitable variables. The resulting system of equations is solved numerically using the Finite Difference Method. The influence of key parameters on velocity, temperature, and concentration distributions is analyzed. Additionally, the study explores the impact of flow resistance and transport phenomena along the hemispherical surface on atmospheric dynamics and their potential role in climate variation. The findings show a novel role of the velocity slip parameters<span>({beta }^{*})</span>, significantly enhances thermal efficiency by reducing boundary layer thickness and improving energy and mass flow. This leads to improve heat ditribution and reduced energy consumption which collectively influence climate change and regulate atmospheric temperature gradients. Moreover, the study introduces insights into the effects of the thermal slip <span>({gamma }^{*},)</span> increasing the thermal slip parameter <span>(,)</span> velocity rises near the surface while dereaseing far from the surface, enhancing heat transfer and thermal regulation, which supports energy savings despite climate implications. The findings indicate that parameters<span>(m)</span>, <span>({Ri}_{T})</span>, <span>({Ri}_{C})</span> and Sc significantly enhance interaction moleculer resistance, heat transfer, and mass transfer rates, emphasizing their key role in optimizing energy usage and stabilizing atmospheric temperature. The physical and numerical behavior of the model is illustrated using both graphical and tabular representations.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148008740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The multiphase-field method based on internal state variables","authors":"Andreas Prahs,&nbsp;Ahmed Elmoghazy,&nbsp;Daniel Schneider,&nbsp;Britta Nestler","doi":"10.1007/s00161-026-01470-8","DOIUrl":"10.1007/s00161-026-01470-8","url":null,"abstract":"<div><p>The multiphase-field method is widely used to simulate the evolution of complex microstructures in computational materials science and is commonly derived via a variational approach. When coupled with heat conduction, it is desirable to derive both the multiphase-field method and the heat conduction equation from a unified, consistent framework. In the present work, this is accomplished by introducing order parameters as internal state variables and exploiting the entropy production inequality of the diffuse interface region for multiple intersecting phases. The approach represents a generalization of the method of Prahs <i>et al.</i> (Prahs <i>et al.</i> <i>Continuum Mech. Thermodyn.</i> <b>37</b>, 55 (2025). https://doi.org/10.1007/s00161-025-01383-y) via a dual-interaction ansatz and its Lagrange multiplier simplification, while maintaining thermodynamical consistency. This requirement, in turn, restricts the choice of the interpolation functions. Moreover, the coupling effects in the heat conduction equation as well as connections to established evolution equations from the literature are demonstrated through an illustrative derivation.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-026-01470-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147937947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Corrosion/deformation interplay: a view from electrochemical side","authors":"Galina A. Tsirlina","doi":"10.1007/s00161-026-01466-4","DOIUrl":"10.1007/s00161-026-01466-4","url":null,"abstract":"<div><p>Application of relationships of electrochemical kinetics to determination of corrosion rate is considered in respect to the models of stress effects. Unavoidable limitations and approximations are accented, and typical misunderstandings existing in the literature are discussed. Consideration is limited to corrosion processes resulting from oxidation at material (metal)/solution interface, including atmospheric corrosion in humid environment. For these processes, exponential dependence on stress is only valid if stress is isotropic, and dissolution of material predominates as compared to formation of solid films. Electrochemical tools to identify this type of behavior are considered.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147937954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generalization of R. Hill’s Solution of the Lame Problem for a Hollow Sphere to the Case of Large Elastic and Plastic Deformations","authors":"Vladimir A. Levin,&nbsp;Konstantin M. Zingerman","doi":"10.1007/s00161-026-01479-z","DOIUrl":"10.1007/s00161-026-01479-z","url":null,"abstract":"<div><p>An approximate analytical solution of the Lame problem for a hollow sphere is obtained for isotropic compressible elastoplastic materials under large elastic and plastic deformations. This solution generalizes the known solution by R. Hill [1] to the case when not only plastic but also elastic deformations are large. To describe elastic deformations, nonlinear constitutive relations previously proposed by the authors are used, which reduce to the Murnaghan equation of state in the case of purely volumetric deformation. To describe plastic deformations, two models of ideal plasticity theory are used: a model based on the Mises yield criterion and the associated flow rule, and a model based on the Drucker–Prager yield criterion and a non-associated flow rule. For these classes of materials, approximate analytical solutions of the Lame problem under large elastic and plastic deformations are obtained. Nonlinear effects and effects due to plasticity are investigated. One of these effects is that there is a limiting pressure that can be applied to the inner boundary of the hollow sphere. Another effect is that the solution for given pressure can be not unique. The detailed analysis is performed for the case in which the hollow sphere is expanded under the action of pressure applied to its internal boundary.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147937951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Statistical aspects of estimating density of penny-shaped inhomogeneities from their intersections with plane sections and lines","authors":"Yulia Pronina","doi":"10.1007/s00161-026-01474-4","DOIUrl":"10.1007/s00161-026-01474-4","url":null,"abstract":"<div><p>Quantitative evaluation of 3D density of cracks or plates from the data on their intersections with the 2D plane of a polish or a section may serve as a tool for monitoring changes in the effective elastic and conductive properties of materials due to such defects. In previous works co-authored with Mark Kachanov, relationships were established between the 3D density of flat circular cracks or thin plates and the 2D density of their line traces observed on the surfaces of sections; the latter parameter being defined as the sum of the trace half-lengths squared per unit area. In the present paper, the estimate of the 3D crack density, in the isotropic case, was derived using other parameters — numbers of the defect intersections with a plane section and a line — which are easier to determine experimentally than the crack trace lengths. The mentioned relationships were obtained in terms of mathematical expectations; therefore, estimates of the 3D density of cracks or plates, calculated using observed data are spread out around the actual values. Formulas for the dispersion measures of the crack density estimates were derived and analysed depending on various geometric parameters. In particular, it was shown in which cases the variance increases with an increase in the number of observed crack traces, that may seem counterintuitive.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147937950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}